Details

analyze463.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample47.0ms

Algorithm

intervals

Results

12.0ms	35×	body	2560	valid
8.0ms	154×	body	80	valid
8.0ms	32×	body	1280	valid
3.0ms	16×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	24×	body	80	nan
1.0ms	3×	body	5120	valid
1.0ms	17×	body	80	invalid
0.0ms	4×	body	160	valid

simplify203.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (202.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 36.7b

Counts

2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

10.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
4.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify39.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5340	1316

prune169.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	76	8	84

Merged error: 5.1b

Counts

84 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `div-exp`
8×	`pow1` `add-log-exp`
7×	`add-cube-cbrt`
6×	`prod-exp`
4×	`cbrt-undiv` `sqrt-prod`
3×	`rec-exp` `flip3--` `times-frac` `1-exp` `flip--` `associate-/l*`
2×	`sub-neg` `pow-flip` `sqrt-div` `diff-log` `cbrt-unprod` `difference-of-squares`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `div-inv` `distribute-lft-out--` `inv-pow`

Counts

4 → 73

Calls

4 calls:

13.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
4.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series74.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify40.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4995	1244
1	4995	1244

prune138.0ms

Filtered

57 candidates to 85 candidates (-49.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	82	11	93

Merged error: 5.0b

Counts

93 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 58

Calls

4 calls:

7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4973	1018
1	4973	1018

prune163.0ms

Filtered

56 candidates to 70 candidates (-25.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	70	11	81

Merged error: 5.0b

Counts

81 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.1b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 69

Calls

4 calls:

12.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
4.0ms	(- (* b b) (* (* 4.0 a) c))
10.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify39.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5863	1224

prune104.0ms

Filtered

61 candidates to 81 candidates (-32.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	82	10	92

Merged error: 4.9b

Counts

92 → 10

regimes492.0ms

Accuracy

85.7% (3.9b remaining)

Error of 9.4b against oracle of 5.6b and baseline of 32.6b

bsearch96.0ms

Steps

Iters	Range	Point
8	1.6867471081690859e-50	2.5447835009091082e-46	1.7437407699301904e-49
10	1.509572647784613e-212	1.0810837518264463e-201	2.234284491165597e-207
9	-8.883143262175477e+108	-1.2726239932034528e+104	-3.5005804636134674e+108

Iters

Range

Point

1.6867471081690859e-50

2.5447835009091082e-46

1.7437407699301904e-49

1.509572647784613e-212

1.0810837518264463e-201

2.234284491165597e-207

-8.883143262175477e+108

-1.2726239932034528e+104

-3.5005804636134674e+108

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	117	67
1	117	67

end0.0ms

sample1.3s

Algorithm

intervals

Results

323.0ms	1047×	body	2560	valid
272.0ms	5137×	body	80	valid
233.0ms	919×	body	1280	valid
94.0ms	461×	body	640	valid
45.0ms	117×	body	5120	valid
36.0ms	667×	body	80	nan
32.0ms	208×	body	320	valid
19.0ms	368×	body	80	invalid
11.0ms	111×	body	160	valid

Details

analyze463.0ms

sample47.0ms

simplify203.0ms

prune11.0ms

localize11.0ms

rewrite27.0ms

series65.0ms

simplify39.0ms

prune169.0ms

localize15.0ms

rewrite31.0ms

series74.0ms

simplify40.0ms

prune138.0ms

localize14.0ms

rewrite25.0ms

series64.0ms

simplify50.0ms

prune163.0ms

localize12.0ms

rewrite31.0ms

series63.0ms

simplify39.0ms

prune104.0ms

regimes492.0ms

bsearch96.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling